We prove global Lipschitz regularity for a wide class of convex variational integrals among all functions in $W^{1,1}$ with prescribed (sufficiently regular) boundary values, which are not assumed to satisfy any geometrical constraint (as for example bounded slope condition). Furthermore, we do not assume any restrictive assumption on the geometry of the domain and the result is valid for all sufficiently smooth domains. The result is achieved with a suitable approximation of the functional together with a new construction of appropriate barrier functions.
A boundary regularity result for minimizers of variational integrals with nonstandard growth / Bulicek, M.; Maringova, E.; Stroffolini, B.; Verde, A.. - In: NONLINEAR ANALYSIS. - ISSN 1873-5215. - on-line 28 marzo 2018:(2018). [10.1016/j.na.2018.03.001]
A boundary regularity result for minimizers of variational integrals with nonstandard growth
B. StroffoliniMembro del Collaboration Group
;A. VerdeMembro del Collaboration Group
2018
Abstract
We prove global Lipschitz regularity for a wide class of convex variational integrals among all functions in $W^{1,1}$ with prescribed (sufficiently regular) boundary values, which are not assumed to satisfy any geometrical constraint (as for example bounded slope condition). Furthermore, we do not assume any restrictive assumption on the geometry of the domain and the result is valid for all sufficiently smooth domains. The result is achieved with a suitable approximation of the functional together with a new construction of appropriate barrier functions.File | Dimensione | Formato | |
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